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- Suppose a continuous random variable X pdf constant from 0 to 7.516, where the pdf is zero elsewhere. what is variance of this random variable?Suppose that n observations are chosen at random from a continuous pdf fY(y). What is the probability that the last observation recorded will be the smallest number in the sample?Estimate MSE of variance for x and Y
- If the variance of a continuous random variable X with pdf f(x) is noted as V(X), what is its standard deviation?Records for the last 15 years have shown that the average rainfall in a certain region of the country, for the month of March, to be 1.20 inches, with s = 0.45 inches. A second region had an average rainfall of 1.35 inches, with s = 0.54. estimate the difference of the true average rainfalls in those two regions as a 95% C.I. with the assumption of normal populations and unequal variances.solve the problem in the photo using normal distribution laws
- Suppose that the lifetime, X, and brightness, Y, of a light bulb are modeled as continuous random variables. Let their joint pdf be given by:f(x,y)=λ_1λ_2e^{-λ_1x-λ_2y},x,y>0 •Are lifetime and brightness independent?•Are lifetime and brightness uncorrelated?In a fish restaurant, population variance for fish to go bad is at least 4 days. After buying a new cooling system, its expected to be less than 4 days. After buying the new cooling system, 10 fish are tested and with an average of 8 days without going bad with a population variance of 3 days. Test with 95 confidince if the population variance is really less than 4 days. (use chi square please)If Y1,...,Yn denote a random sample of sizenfrom the normal distribution with known mean μ and variance σ2= 25, find the method of moment estimator of μ.